I have a couple in the White Mountains.
There are a couple areas in the Twin Mountain/Bretton Woods area with primitive camping. They are basically just a clearing with a fire ring, nothing else. Some can be driven into and others are a short walk (50-100 feet) from the road. The sites are spread out and tend to be very quiet. However, there are no amenities. Hot showers and real bathrooms are available at the AMC Highland Center or Conway Railroad station in Crawford Notch. The only hangup here is that they are first come, first served. Going up mid-week I have never had a problem getting a site but they usually fill up on Friday evening.
If you want something with facilities and will take reservations, I like Dry River Campground just east of Crawford Notch on RT302. It is a relatively small campground, quiet, with restroom/shower/laundry facilities. There is a great place to swim in the river about 1/2 mile up the road. There is also some hiking trails out the back of the campground. I have stayed here many times, especially when my kids were active in Cub Scouts. The sites are close together but they will all accommodate vehicles and some will accommodate small campers or vehicle/trailer combos.
Though I have been to Acadia, I have never camped in the area. I can tell you, though, it is a high tourist area in the summer and very busy.
When are you planning to make this trip?